I have at least 2 options. First, drive on forwards and put the bucket over the rail on the tongue. Second drive on backwards with the mower suspended from the FEL. The latter, I am 90% certain will work.
That's exactly what I do, as I have the same tractor (same chassis, 6 fewer horses) and the same size trailer. I have indeed transported my tractor with brush cutter, and getting the weight balanced was not impossible, but did probably take me a few tries of configuration to get it right. That was a few years back, and I've hauled it in enough other configurations now that I don't remember exactly what I did.
I can say I almost never use my brush cutter
and FEL together, so I may have left the bucket or even entire FEL at home. In other cases, I've been known to drop the bucket way up at the front of the trailer, and then back the rest of the rig on after. Another option you already named is to put the brush cutter under the FEL, which especially if you're dropping the bucket up front, can be done pretty easily and safely.
All of this is kind of a PITA, as I think I already said in my first post in this thread, but it works perfectly fine and is the compromise you make for the convenience of towing a smaller trailer in tight spaces. Everything is a trade-off, and the right trailer for one guy is not always the right one for the next, even when hauling the same equipment, depending on frequency and variability of configurations.
Winter Deere. You are certainly right about the need for tiedown loops in the front. I wonder how JD transports them?
I was just looking at the weight bar. It's about 1 3/8 square steel. I could loop the chain over that, but it could slide sideways a bit. Thinking about that one some more though. There is a way to do this.
I have a handful of 2" heavy duty nylon strap loops, I think they came off a Bell Telephone truck and were used for pulling telephone poles. I loop one or two of them thru that front weight bar in a choker type configuration, and then hook my ratchet strap hooks onto those in a way they can never come undone (feed thru hook and double it back on itself). If you're tucking your brush cutter under the loader, I'd probably leave the bucket off (or parked up front on trailer), and then route these straps under the loader. That way, you can lower the loader onto them, which might keep it off the brush cutter without additional blocking.
I've complained a lot about Deere's lack of towing hooks on the front of these tractors, but I've been told nearly all brands are equally bad, on this point.